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31 Write the ratios for sin C, cos C and tan C. A 25 7 24 Note: Use slash (/) to separate numerator and denominator. sin C Cos C tan C

31 Write the ratios for sin C, cos C and tan C. A 25 7 24 Note: Use slash (/) to separate numerator and denominator. sin C Cos C tan C

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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31. Write the rations for Sin C, cos C, and tan c.
### Question 31/36 #### Write the ratios for \(\sin C\), \(\cos C\) and \(\tan C\). A right-angled triangle \( \triangle ABC \) is shown with: - The length of side \( AB \) = 7 - The length of side \( BC \) = 24 - The length of the hypotenuse \( AC \) = 25 ``` A | |\ 7 | \ 25 | \ | \ |_____\ C B 24 ``` *Note: Use slash (/) to separate the numerator and denominator.* - **\(\sin C\)** (Sine of angle \(C\)) = Opposite / Hypotenuse - **\(\cos C\)** (Cosine of angle \(C\)) = Adjacent / Hypotenuse - **\(\tan C\)** (Tangent of angle \(C\)) = Opposite / Adjacent | Term | Ratio | |-------|---------------| | \(\sin C\) | [__________] | | \(\cos C\) | [__________] | | \(\tan C\) | [__________] | #### Explanation: 1. **\(\sin C\)**: This is the ratio of the length of the side opposite angle \( C \) to the hypotenuse. Here, the opposite side to angle \( C \) is \( AB \), and the hypotenuse is \( AC \). 2. **\(\cos C\)**: This is the ratio of the length of the side adjacent to angle \( C \) to the hypotenuse. Here, the adjacent side to angle \( C \) is \( BC \), and the hypotenuse is \( AC \). 3. **\(\tan C\)**: This is the ratio of the length of the side opposite angle \( C \) to the side adjacent to angle \( C \). Here, the opposite side to angle \( C \) is \( AB \), and the adjacent side to angle \( C \) is \( BC \). Fill in the provided boxes with the appropriate ratios to complete this exercise.
Transcribed Image Text:### Question 31/36 #### Write the ratios for \(\sin C\), \(\cos C\) and \(\tan C\). A right-angled triangle \( \triangle ABC \) is shown with: - The length of side \( AB \) = 7 - The length of side \( BC \) = 24 - The length of the hypotenuse \( AC \) = 25 ``` A | |\ 7 | \ 25 | \ | \ |_____\ C B 24 ``` *Note: Use slash (/) to separate the numerator and denominator.* - **\(\sin C\)** (Sine of angle \(C\)) = Opposite / Hypotenuse - **\(\cos C\)** (Cosine of angle \(C\)) = Adjacent / Hypotenuse - **\(\tan C\)** (Tangent of angle \(C\)) = Opposite / Adjacent | Term | Ratio | |-------|---------------| | \(\sin C\) | [__________] | | \(\cos C\) | [__________] | | \(\tan C\) | [__________] | #### Explanation: 1. **\(\sin C\)**: This is the ratio of the length of the side opposite angle \( C \) to the hypotenuse. Here, the opposite side to angle \( C \) is \( AB \), and the hypotenuse is \( AC \). 2. **\(\cos C\)**: This is the ratio of the length of the side adjacent to angle \( C \) to the hypotenuse. Here, the adjacent side to angle \( C \) is \( BC \), and the hypotenuse is \( AC \). 3. **\(\tan C\)**: This is the ratio of the length of the side opposite angle \( C \) to the side adjacent to angle \( C \). Here, the opposite side to angle \( C \) is \( AB \), and the adjacent side to angle \( C \) is \( BC \). Fill in the provided boxes with the appropriate ratios to complete this exercise.
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